Can you please give examples in the config of what syntax is used with the weak sky renders config to get the mod to work with Botania's GoG skybox?

same as 'skySupportedDimensions'. The comment on the config option also tells you that it's a list of dimension ID's

Config setup:

Whitelist of dimension ID's that will have special sky rendering + constellation handling (and thus starlight collection, ...) [default: [0]]

S:skySupportedDimensions <
    0
 >

# Defines how much the 'sharpened' modifier increases the damage of the sword if applied. Config value is in percent. [range: 0.0 ~ 10000.0, default: 0.1]
S:swordSharpenedMultiplier=0.1

# IF a dimensionId is listed in 'skySupportedDimensions' you can addAmount it here to keep its sky render, but AS will try to render only constellations on top of its existing sky render. [default: ]
S:weakSkyRenders <
    0
 >

}

If the syntax is wrong, please inform me of how it should be setup.

Simply putting 0 in the weak sky renders config area does nothing.

Can you provide a copy of your config and a screenshot of it not working please.

Alright, with the latest version (1.2.3 beta) and the above config setup, I have confirmed that the mod does work with Botania's Fancy Skybox.

Screenshot: https://www.dropbox.com/s/x8ciom1dk5zkx31/2017-03-20_09.39.56.png?dl=0